Common Fixed Point of Generalized Berinde Type Contraction and an Application

Abstract

In this paper, we introduce $\lambda_{(s,\varphi,\psi,L)}$-generalized Berinde type contraction and obtain some common fixed point results for such class of contractions the setting of triangular $\alpha$-admissible mappings with respect to $\eta$ in the framework of $b$-metric spaces. Our results generalize and extend some theorems in the literature. An example is given to support our result.